Find the minimum number of points required to earn a grade of "A" on the exam.

Question

The final exam given to a lecture section of Statistics 1 at a large university is graded "on a curve." The professor decides to assign the top 12% of the grades A's, the next 22% will be assigned B's, the middle 32%will be assigned C's, the next 22% will receive D's, and the bottom 12% will earn F's. The Points earned by the students are approximately normally distributed with a mean of 90 points and a standard deviation of 16 points

Answer 1

Even though the "Points" say 90. Don't get confused with 90 = A because this test is most likely not out of 100 points.

 

Find the Z score for the top 12%.

You might have to do 100%-12% to get the Z score you want.

 

A Z score represents the number of standard deviations away from the mean.

After getting your Z score, You need to turn that into points.

 

Say you have a Z-score of +1.5 for example. Then the number of points from the mean would be 1.5*16 = 24 points.

This represents how far from the mean your score should be. So add that to the mean. 90+124 = 114 points.

 

OK, now look up the actual z-score and get the answer with the actual numbers.